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A174114 Even central polygonal numbers (A193868) divided by 2. 9
1, 2, 8, 11, 23, 28, 46, 53, 77, 86, 116, 127, 163, 176, 218, 233, 281, 298, 352, 371, 431, 452, 518, 541, 613, 638, 716, 743, 827, 856, 946, 977, 1073, 1106, 1208, 1243, 1351, 1388, 1502, 1541, 1661, 1702, 1828, 1871, 2003, 2048, 2186, 2233, 2377, 2426, 2576 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Central terms of A170950, seen as a triangle of rows with an odd number of terms.

Equivalently, numbers of the form m*(4*m+3)+1, where m = 0, -1, 1, -2, 2, -3, 3, ... [Bruno Berselli, Jan 05 2016]

LINKS

Table of n, a(n) for n=1..51.

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

FORMULA

a(n+3) - a(n+2) - a(n+1) + a(n) = A010696(n+1).

a(n) = A170950(A002061(n)).

a(n) = A193868(n)/2. - Omar E. Pol, Aug 16 2011

G.f. -x*(1+x+4*x^2+x^3+x^4) / ( (1+x)^2*(x-1)^3 ). - R. J. Mathar, Aug 18 2011

MATHEMATICA

Select[Table[(n (n + 1)/2 + 1)/2, {n, 600}], IntegerQ] (* Vladimir Joseph Stephan Orlovsky, Feb 06 2012 *)

(Select[PolygonalNumber@ Range@ 100, OddQ] + 1 )/2 (* Version 10.4, or *)

Rest@ CoefficientList[Series[-x (1 + x + 4 x^2 + x^3 + x^4)/((1 + x)^2 (x - 1)^3), {x, 0, 50}], x] (* Michael De Vlieger, Jun 30 2016 *)

PROG

(PARI) a(n)=(2*n-1)*(2*n-1-(-1)^n)\4+1 \\ Charles R Greathouse IV, Jun 11 2015

CROSSREFS

Cf. A002522.

Cf. A033951: numbers of the form m*(4*m+3)+1 for nonnegative m.

Sequence in context: A189328 A090746 A234924 * A197540 A089118 A146480

Adjacent sequences:  A174111 A174112 A174113 * A174115 A174116 A174117

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Mar 08 2010

EXTENSIONS

New name from Omar E. Pol, Aug 16 2011

STATUS

approved

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Last modified October 18 01:01 EDT 2018. Contains 316297 sequences. (Running on oeis4.)