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A261191 40-gonal numbers: a(n) = 38*n*(n-1)/2 + n. 5
0, 1, 40, 117, 232, 385, 576, 805, 1072, 1377, 1720, 2101, 2520, 2977, 3472, 4005, 4576, 5185, 5832, 6517, 7240, 8001, 8800, 9637, 10512, 11425, 12376, 13365, 14392, 15457, 16560, 17701, 18880, 20097, 21352, 22645, 23976, 25345, 26752, 28197, 29680, 31201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

According to the common formula for the polygonal numbers: (s-2)*n*(n-1)/2 + n (here s = 40).

The 4th number of the sequence, 117, is also the 10th pentagonal number (see A000326). The next number of the series, 232, is also the 9th decagonal number (see A001107), while 576 is the 25th square number (see A000290). The 12th number of the sequence, 2101, is the 23rd 11-gonal number (see A051682).

From Bruno Berselli, Aug 21 2015: (Start)

a(n) and a(n) - 2*n + 1 provide the numbers m such that 19*m + 81 is a square.

Partial sums of the numbers of the type 38*h + 1 (quadrisections of A113541 and A151979). (End)

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index to sequences related to polygonal numbers

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

FORMULA

a(n) = n*(19*n - 18).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), for n > 2. - Colin Barker, Aug 11 2015

G.f.: -x*(37*x+1) / (x-1)^3. - Colin Barker, Aug 11 2015

MAPLE

A261191:=n->38*n*(n-1)/2+n: seq(A261191(n), n=0..50); # Wesley Ivan Hurt, Aug 15 2015

MATHEMATICA

Table[n (19 n - 18), {n, 0, 45}] (* Bruno Berselli, Aug 21 2015 *)

PROG

(JavaScript) function a(n){return 38*n*(n-1)/2+n}

(PARI) concat(0, Vec(-x*(37*x+1)/(x-1)^3 + O(x^100))) \\ Colin Barker, Aug 11 2015

(PARI) first(m)=my(v=vector(m, i, i--; 38*i*(i-1)/2+i)); v; \\ Anders Hellström, Aug 13 2015

(MAGMA) [n*(19*n-18): n in [0..45]]; // Vincenzo Librandi, Aug 12 2015

CROSSREFS

Sequence in context: A235893 A192791 A235886 * A260601 A234921 A199807

Adjacent sequences:  A261188 A261189 A261190 * A261192 A261193 A261194

KEYWORD

nonn,easy

AUTHOR

Sergey Pavlov, Aug 11 2015

STATUS

approved

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Last modified February 26 11:02 EST 2021. Contains 341631 sequences. (Running on oeis4.)