A022285 -id:A022285

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A022289

a(n) = n*(31*n + 1)/2.

+10
16

0, 16, 63, 141, 250, 390, 561, 763, 996, 1260, 1555, 1881, 2238, 2626, 3045, 3495, 3976, 4488, 5031, 5605, 6210, 6846, 7513, 8211, 8940, 9700, 10491, 11313, 12166, 13050, 13965, 14911, 15888, 16896, 17935

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

FORMULA

a(n) = 31*n + a(n-1) - 15, for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

G.f.: x*(16 + 15*x)/(1 - x)^3 . - R. J. Mathar, Sep 02 2016

a(n) = A000217(16*n) - A000217(15*n). In general, n*((2*k+1)*n + 1)/2 = A000217((k+1)*n) - A000217(k*n). - Bruno Berselli, Oct 13 2016

E.g.f.: (x/2)*(31*x + 32)*exp(x). - G. C. Greubel, Aug 23 2017

MATHEMATICA

Table[n (31 n + 1)/2, {n, 0, 40}] (* Bruno Berselli, Oct 13 2016 *)

LinearRecurrence[{3, -3, 1}, {0, 16, 63}, 40] (* Harvey P. Dale, Aug 10 2019 *)

PROG

(PARI) a(n)=n*(31*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. similar sequences of the form n*((2*k+1)*n + 1)/2: A000217 (k=0), A005449 (k=1), A005475 (k=2), A022265 (k=3), A022267 (k=4), A022269 (k=5), A022271 (k=6), A022273 (k=7), A022275 (k=8), A022277 (k=9), A022279 (k=10), A022281 (k=11), A022283 (k=12), A022285 (k=13), A022287 (k=14), this sequence (k=15).

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

A022284

a(n) = n*(27*n - 1)/2.

+10
3

0, 13, 53, 120, 214, 335, 483, 658, 860, 1089, 1345, 1628, 1938, 2275, 2639, 3030, 3448, 3893, 4365, 4864, 5390, 5943, 6523, 7130, 7764, 8425, 9113, 9828, 10570, 11339, 12135, 12958, 13808, 14685, 15589

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

FORMULA

a(n) = a(n-1) + 27*n - 14 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

G.f.: x*(13 + 14*x)/(1 - x)^3 . - R. J. Mathar, Aug 04 2016

a(n) = A000217(14*n-1) - A000217(13*n-1). - Bruno Berselli, Oct 14 2016

E.g.f.: (x/2)*(27*x + 26)*exp(x). - G. C. Greubel, Aug 23 2017

MATHEMATICA

Table[n (27 n - 1)/2, {n, 0, 40}] (* Bruno Berselli, Oct 14 2016 *)

LinearRecurrence[{3, -3, 1}, {0, 13, 53}, 40] (* Harvey P. Dale, Jul 04 2022 *)

PROG

(PARI) a(n)=n*(27*n-1)/2 \\ Charles R Greathouse IV, Jun 17 2017