A145919 A000332(n) = a(n)*(3*a(n) - 1)/2.

0, 0, 0, 0, 1, 2, -3, 5, 7, -9, 12, 15, -18, 22, 26, -30, 35, 40, -45, 51, 57, -63, 70, 77, -84, 92, 100, -108, 117, 126, -135, 145, 155, -165, 176, 187, -198, 210, 222, -234, 247, 260, -273, 287, 301, -315, 330, 345, -360, 376, 392, -408, 425, 442, -459, 477

Offset

0,6

Comments

As the formula in the description shows, all members of A000332 belong to the generalized pentagonal sequence (A001318). A001318 also lists all nonnegative numbers that belong to A145919.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Pentagonal Number.

Eric Weisstein's World of Mathematics, Pentatope Number.

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Formula

a(n+3) = A001840(n) when 3 does not divide n, A001840(n)*-1 otherwise.

After first two zeros, this sequence consists of all values of A001318(n) and A045943(n)*(-1), n>=0, sorted in order of increasing absolute value.

G.f.: (-x^4*(x^4+2*x^3-3*x^2+2*x+1))/((x-1)^3*(1+x^2+x)^3). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

Example

a(6) = -3 and A000332(6) = (-3)(-10)/2 = 15.

Mathematica

CoefficientList[Series[(-x^4*(x^4 + 2*x^3 - 3*x^2 + 2*x + 1))/((x - 1)^3*(1 + x^2 + x)^3), {x, 0, 50}], x] (* G. C. Greubel, Jun 13 2017 *)
LinearRecurrence[{0, 0, 3, 0, 0, -3, 0, 0, 1}, {0, 0, 0, 0, 1, 2, -3, 5, 7}, 60] (* Harvey P. Dale, Feb 13 2023 *)

Prog

(PARI) x='x+O('x^50); concat([0, 0, 0, 0], Vec((-x^4*(x^4 +2*x^3 -3*x^2 +2*x +1))/((x-1)^3*(1+x^2+x)^3))) \\ G. C. Greubel, Jun 13 2017

Crossrefs

Cf. A000326, A145920.

Sequence in context: A071423 A211004 A062781 * A058937 A130518 A001840

Adjacent sequences: A145916 A145917 A145918 * A145920 A145921 A145922

Keyword

easy,sign

Author

Matthew Vandermast, Oct 28 2008

Status

approved