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 A266677 Alternating sum of hexagonal pyramidal numbers. 5
 0, -1, 6, -16, 34, -61, 100, -152, 220, -305, 410, -536, 686, -861, 1064, -1296, 1560, -1857, 2190, -2560, 2970, -3421, 3916, -4456, 5044, -5681, 6370, -7112, 7910, -8765, 9680, -10656, 11696, -12801, 13974, -15216, 16530, -17917, 19380, -20920, 22540 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS More generally, the ordinary generating function for the alternating sum of k-gonal pyramidal numbers is x*(1 + (3 - k)*x)/((x - 1)*(x + 1)^4). LINKS Ilya Gutkovskiy, Extended graphic representation OEIS Wiki, Figurate numbers Eric Weisstein's World of Mathematics, Pyramidal Number Eric Weisstein's World of Mathematics, Hexagonal Pyramidal Number Index entries for linear recurrences with constant coefficients, signature (-3,-2,2,3,1). FORMULA G.f.: x*(1 - 3*x)/((x - 1)*(x + 1)^4). a(n) = ((-1)^n*(2*n*(n + 2)*(4*n + 1) - 3) + 3)/24. a(n) = Sum_{k = 0..n} (-1)^k*A002412(k). MATHEMATICA Table[((-1)^n (2 n (n + 2) (4 n + 1) - 3) + 3)/24, {n, 0, 40}] LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 6, -16, 34}, 40] PROG (PARI) concat(0, Vec(x*(1 - 3*x)/((x - 1)*(x + 1)^4) + O(x^50))) \\ Michel Marcus, Feb 02 2016 CROSSREFS Cf. A000292, A002412, A002717, A173196. Sequence in context: A118014 A236773 A131820 * A083053 A083046 A192749 Adjacent sequences:  A266674 A266675 A266676 * A266678 A266679 A266680 KEYWORD sign,easy AUTHOR Ilya Gutkovskiy, Feb 02 2016 STATUS approved

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Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)