A269440 Alternating sum of 9-gonal (or decagonal) pyramidal numbers.

0, -1, 9, -25, 55, -100, 166, -254, 370, -515, 695, -911, 1169, -1470, 1820, -2220, 2676, -3189, 3765, -4405, 5115, -5896, 6754, -7690, 8710, -9815, 11011, -12299, 13685, -15170, 16760, -18456, 20264, -22185, 24225, -26385, 28671, -31084, 33630, -36310, 39130

Offset: 0

Author

Ilya Gutkovskiy, Feb 26 2016

Keywords

• sign
• easy

Links

• OEIS Wiki, Figurate numbers
• Eric Weisstein's World of Mathematics, Pyramidal Number
• Index entries for linear recurrences with constant coefficients, signature (-3,-2,2,3,1).

Crossrefs

Cf. A000292, A002717, A007584, A173196, A266677.

Programs

Mathematica

Table[(-1)^n (2 n - 1) ((14 n^2 + 34 n + 15)/48) + 5/16, {n, 0, 40}]
LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 9, -25, 55}, 41]

Formula

G.f.: x*(1 - 6*x)/((x - 1)*(x + 1)^4).

a(n) = (-1)^n*(2*n - 1)*(14*n^2 + 34*n + 15)/48 + 5/16.

a(n) = Sum_{k = 0..n} (-1)^k*A007584(k).