A269441 Alternating sum of 10-gonal (or decagonal) pyramidal numbers.

0, -1, 10, -28, 62, -113, 188, -288, 420, -585, 790, -1036, 1330, -1673, 2072, -2528, 3048, -3633, 4290, -5020, 5830, -6721, 7700, -8768, 9932, -11193, 12558, -14028, 15610, -17305, 19120, -21056, 23120, -25313, 27642, -30108, 32718, -35473, 38380, -41440, 44660

Offset

0,3

Links

Table of n, a(n) for n=0..40.

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).

Formula

G.f.: x*(1 - 7*x)/((x - 1)*(x + 1)^4).

a(n) = ((-1)^n*(16*n^3 + 30*n^2 - 4*n - 9) + 9) /24.

a(n) = Sum_{k = 0..n} (-1)^k*A007585(k).

Sum_{n>=1} 1/a(n) = -0.9251958836055717745244669... . - Vaclav Kotesovec, Feb 26 2016

Mathematica

Table[((-1)^n (16 n^3 + 30 n^2 - 4 n - 9) + 9)/24, {n, 0, 40}]
LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 10, -28, 62}, 41]

Prog

(Magma) [((-1)^n*(16*n^3+30*n^2-4*n-9)+9)/24: n in [0..40]]; // Vincenzo Librandi, Feb 27 2016

Crossrefs

Cf. A000292, A002717, A007585, A173196, A266677, A269428, A269429.

Sequence in context: A054112 A053790 A364694 * A048491 A124703 A333241

Adjacent sequences: A269438 A269439 A269440 * A269442 A269443 A269444

Keyword

easy,sign

Author

Ilya Gutkovskiy, Feb 26 2016

Status

approved