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A195042 Concentric 9-gonal numbers. 8
0, 1, 9, 19, 36, 55, 81, 109, 144, 181, 225, 271, 324, 379, 441, 505, 576, 649, 729, 811, 900, 991, 1089, 1189, 1296, 1405, 1521, 1639, 1764, 1891, 2025, 2161, 2304, 2449, 2601, 2755, 2916, 3079, 3249, 3421, 3600, 3781, 3969, 4159, 4356, 4555, 4761, 4969, 5184, 5401, 5625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also concentric enneagonal numbers or concentric nonagonal numbers.

A016766 and A069131 interleaved.

Partial sums of A056020. - Reinhard Zumkeller, Jan 07 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

FORMULA

a(n) = (9*n^2+5/2*((-1)^n-1))/4.

G.f. -x*(1+7*x+x^2) / ( (1+x)*(x-1)^3 ). a(n)+a(n+1) = A060544(n+1). - R. J. Mathar, Sep 28 2011

PROG

(MAGMA) [(9*n^2+5/2*((-1)^n-1))/4: n in [0..50]]; // Vincenzo Librandi, Sep 29 2011

(Haskell)

a195042 n = a195042_list !! n

a195042_list = scanl (+) 0 a056020_list

-- Reinhard Zumkeller, Jan 07 2012

(PARI) a(n)=(9*n^2+5/2*((-1)^n-1))/4 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Column 9 of A195040.

Cf. A195041, A077221, A195142, A195043.

Sequence in context: A274590 A051811 A034056 * A157034 A198590 A297396

Adjacent sequences:  A195039 A195040 A195041 * A195043 A195044 A195045

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 27 2011

STATUS

approved

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Last modified February 21 07:18 EST 2018. Contains 299390 sequences. (Running on oeis4.)