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A303304 Generalized 25-gonal (or icosipentagonal) numbers: m*(23*m - 21)/2 with m = 0, +1, -1, +2, -2, +3, -3, ... 29
0, 1, 22, 25, 67, 72, 135, 142, 226, 235, 340, 351, 477, 490, 637, 652, 820, 837, 1026, 1045, 1255, 1276, 1507, 1530, 1782, 1807, 2080, 2107, 2401, 2430, 2745, 2776, 3112, 3145, 3502, 3537, 3915, 3952, 4351, 4390, 4810, 4851, 5292, 5335, 5797, 5842, 6325, 6372, 6876, 6925 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Numbers k for which 184*k + 441 is a square. - Bruno Berselli, Jul 10 2018

Partial sums of A317321. - Omar E. Pol, Jul 28 2018

LINKS

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

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

FORMULA

From Colin Barker, Jul 10 2018: (Start)

G.f.: x*(1 + 21*x + x^2) / ((1 - x)^3*(1 + x)^2).

a(n) = n*(23*n + 42)/8 for n even.

a(n) = (23*n - 19)*(n + 1)/8 for n odd.

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.

(End)

MAPLE

seq(coeff(series(x*(x^2+21*x+1)/((1-x)^3*(1+x)^2), x, n+1), x, n), n=0..50); # Muniru A Asiru, Jul 10 2018

MATHEMATICA

CoefficientList[Series[x (1 + 21 x + x^2)/((1 - x)^3*(1 + x)^2), {x, 0, 49}], x] (* or *)

Array[PolygonalNumber[25, (1 - 2 Boole[EvenQ@ #]) Ceiling[#/2]] &, 50, 0] (* Michael De Vlieger, Jul 10 2018 *)

LinearRecurrence[{1, 2, -2, -1, 1}, {0, 1, 22, 25, 67}, 50] (* Robert G. Wilson v, Jul 15 2018 *)

PROG

(PARI) concat(0, Vec(x*(1 + 21*x + x^2) / ((1 - x)^3*(1 + x)^2) + O(x^40))) \\ Colin Barker, Jul 10 2018

(GAP) a:=[0, 1, 22, 25, 67];;  for n in [6..50] do a[n]:=a[n-1]+2*a[n-2]-2*a[n-3]-a[n-4]+a[n-5]; od; a; # Muniru A Asiru, Jul 10 2018

CROSSREFS

Cf. A255184, A317321.

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), this sequence (k=25), A316724 (k=26), A316725 (k=27), A303812 (k=28), A303815 (k=29), A316729 (k=30).

Sequence in context: A108632 A045096 A227408 * A234540 A124177 A260990

Adjacent sequences:  A303301 A303302 A303303 * A303305 A303306 A303307

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Jul 10 2018

STATUS

approved

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Last modified June 16 03:44 EDT 2019. Contains 324145 sequences. (Running on oeis4.)