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A255178
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Second differences of eighth powers (A001016).
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5
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1, 254, 6050, 52670, 266114, 963902, 2796194, 6927230, 15257090, 30683774, 57405602, 101263934, 170126210, 274309310, 427043234, 644975102, 948713474, 1363412990, 1919399330, 2652834494, 3606422402, 4830154814, 6382097570, 8329217150, 10748247554
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 + x)*(1 + 246*x + 4047*x^2 + 11572*x^3 + 4047*x^4 + 246*x^5 + x^6)/(1 - x)^7.
a(n) = 2*(28*n^6 + 70*n^4 + 28*n^2 + 1) for n>0, a(0)=1.
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EXAMPLE
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Second differences: 1, 254, 6050, 52670, 266114, ... (this sequence)
First differences: 1, 255, 6305, 58975, 325089, ... (A022524)
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The eighth powers: 1, 256, 6561, 65536, 390625, ... (A001016)
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First partial sums: 1, 257, 6818, 72354, 462979, ... (A000542)
Second partial sums: 1, 258, 7076, 79430, 542409, ... (A253636)
Third partial sums: 1, 259, 7335, 86765, 629174, ... (A254642)
Fourth partial sums: 1, 260, 7595, 94360, 723534, ... (A254647)
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MATHEMATICA
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Join[{1}, Table[2 (28 n^6 + 70 n^4 + 28 n^2 + 1), {n, 1, 30}]]
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PROG
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(Magma) [n eq 0 select 1 else 2*(28*n^6+70*n^4+28*n^2+1): n in [0..30]]; // Vincenzo Librandi, Mar 12 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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