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A081438 Diagonal in array of n-gonal numbers A081422. 5
1, 11, 36, 82, 155, 261, 406, 596, 837, 1135, 1496, 1926, 2431, 3017, 3690, 4456, 5321, 6291, 7372, 8570, 9891, 11341, 12926, 14652, 16525, 18551, 20736, 23086, 25607, 28305, 31186, 34256, 37521, 40987, 44660, 48546, 52651, 56981, 61542, 66340 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

One of a family of sequences with palindromic generators.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = (2*n^3+9*n^2+9*n+2)/2.

G.f.: (1+6*x-9*x^2+2*x^3)/(1-x)^5.

From Bruno Berselli, Jun 04 2010: (Start)

G.f.: (1+7*x-2*x^2)/(1-x)^4 (simplified).

a(n) = (n+1)*(2*n^2+7*n+2)/2.

a(n) -4*a(n-1) +6*a(n-2) -4*a(n-3) +a(n-4) = 0, with n>3.

a(n) = (A177058(n+3) + A177058(n+2))/2. (End)

E.g.f.: (1/2)*exp(x)*(2 +20*x + 15*x^2 + 2*x^3). - Stefano Spezia, Aug 15 2019

MAPLE

seq((2*n^3+9*n^2+9*n+2)/2, n=0..45); # G. C. Greubel, Aug 14 2019

MATHEMATICA

CoefficientList[Series[(1 +6x -9x^2 +2x^3)/(1-x)^5, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 08 2013 *)

PROG

(MAGMA) [(2*n^3+9*n^2+9*n+2)/2: n in [0..45]]; // Vincenzo Librandi, Aug 08 2013

(PARI) vector(45, n, n--; (2*n^3+9*n^2+9*n+2)/2) \\ G. C. Greubel, Aug 14 2019

(Sage) [(2*n^3+9*n^2+9*n+2)/2 for n in (0..45)] # G. C. Greubel, Aug 14 2019

(GAP) List([0..45], n-> (2*n^3+9*n^2+9*n+2)/2); # G. C. Greubel, Aug 14 2019

CROSSREFS

Cf. A081436, A081437, A081441, A177058.

Sequence in context: A044469 A015246 A093500 * A160483 A034309 A005000

Adjacent sequences:  A081435 A081436 A081437 * A081439 A081440 A081441

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 21 2003

STATUS

approved

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Last modified April 4 07:32 EDT 2020. Contains 333213 sequences. (Running on oeis4.)