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A303812 Generalized 28-gonal (or icosioctagonal) numbers: m*(13*m - 12) with m = 0, +1, -1, +2, -2, +3, -3, ... 28
0, 1, 25, 28, 76, 81, 153, 160, 256, 265, 385, 396, 540, 553, 721, 736, 928, 945, 1161, 1180, 1420, 1441, 1705, 1728, 2016, 2041, 2353, 2380, 2716, 2745, 3105, 3136, 3520, 3553, 3961, 3996, 4428, 4465, 4921, 4960, 5440, 5481, 5985, 6028, 6556, 6601, 7153, 7200, 7776, 7825, 8425, 8476, 9100, 9153 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of A317324. - Omar E. Pol, Jul 28 2018

LINKS

Table of n, a(n) for n=0..53.

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

G.f.: x*(1 + 24*x + x^2) / ((1 + x)^2*(1 - x)^3). - Vincenzo Librandi, Jun 23 2018

MATHEMATICA

With[{nn = 54, s = 28}, {0}~Join~Riffle[Array[PolygonalNumber[s, #] &, Ceiling[nn/2]], Array[PolygonalNumber[s, -#] &, Ceiling[nn/2]]]] (* Michael De Vlieger, Jun 14 2018 *)

CoefficientList[Series[x (1 + 24 x + x^2) / ((1 + x)^2 (1 - x)^3), {x, 0, 60}], x] (* Vincenzo Librandi, Jun 23 2018 *)

PROG

(MAGMA) I:=[0, 1, 25, 28, 76]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..60]]; // Vincenzo Librandi, Jun 23 2018

CROSSREFS

Cf. A161935, A303814, A303815, A317324.

Sequences of generalized k-gonal numbers: A001318 (k=5), A000217 (k=6), A085787 (k=7), A001082 (k=8), A118277 (k=9), A074377 (k=10), A195160 (k=11), A195162 (k=12), A195313 (k=13), A195818 (k=14), A277082 (k=15), A274978 (k=16), A303305 (k=17), A274979 (k=18), A303813 (k=19), A218864 (k=20), A303298 (k=21), A303299 (k=22), A303303 (k=23), A303814 (k=24), A303304 (k=25), A316724 (k=26), A316725 (k=27), this sequence (k=28), A303815 (k=29), A316729 (k=30).

Sequence in context: A254226 A195613 A127652 * A259028 A317392 A234640

Adjacent sequences:  A303809 A303810 A303811 * A303813 A303814 A303815

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Jun 12 2018

STATUS

approved

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Last modified April 1 10:33 EDT 2020. Contains 333159 sequences. (Running on oeis4.)