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A081435 Diagonal in array of n-gonal numbers A081422. 8
1, 5, 18, 46, 95, 171, 280, 428, 621, 865, 1166, 1530, 1963, 2471, 3060, 3736, 4505, 5373, 6346, 7430, 8631, 9955, 11408, 12996, 14725, 16601, 18630, 20818, 23171, 25695, 28396, 31280, 34353, 37621, 41090, 44766, 48655, 52763, 57096, 61660 (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 +3*n^2 +3*n +2)/2.

G.f.: (1 +3*x^2 -4*x^3)/(1-x)^5.

MATHEMATICA

Table[(n^3 + (n + 1)^3 - 1)/2 + 1, {n, 0, 70}] (* Vladimir Joseph Stephan Orlovsky, May 04 2011 *)

CoefficientList[Series[(1 + 3 x^2 - 4 x^3)/(1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 08 2013 *)

PROG

(MAGMA) [(2*n^3+3*n^2+3*n+2)/2: n in [0..50]]; // Vincenzo Librandi, Aug 08 2013

CROSSREFS

Cf. A081434, A081436, A081437.

Sequence in context: A000339 A270944 A272457 * A272748 A273559 A272792

Adjacent sequences:  A081432 A081433 A081434 * A081436 A081437 A081438

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 21 2003

STATUS

approved

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Last modified October 17 16:42 EDT 2018. Contains 316286 sequences. (Running on oeis4.)