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A154105 a(n) = 12*n^2 + 18*n + 7. 3
7, 37, 91, 169, 271, 397, 547, 721, 919, 1141, 1387, 1657, 1951, 2269, 2611, 2977, 3367, 3781, 4219, 4681, 5167, 5677, 6211, 6769, 7351, 7957, 8587, 9241, 9919, 10621, 11347, 12097, 12871, 13669, 14491, 15337, 16207, 17101, 18019, 18961, 19927, 20917, 21931 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is the number of partitions with three integral dissimilar components of the number 12(n+1), e.g for n=0, 12 may be partitioned in the 7 ways (1,2,9), (1,3,8), (1,4,7), (1,5,6), (2,3,7), (2,4,6) and (3,4,5). - Ian Duff, Jan 31 2010

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

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

FORMULA

G.f.: (7 + 16*x + x^2)/(1-x)^3.

a(n) = 6*A014106(n) + 7.

a(0) = 7; for n > 0, a(n) = a(n-1) + 24*n + 6.

a(-n-1) = 2*A085473(n) - 1. - Bruno Berselli, Sep 05 2011

E.g.f.: (7 + 30*x + 12*x^2)*exp(x). - G. C. Greubel, Sep 02 2016

EXAMPLE

a(2) = 12*2^2 + 18*2 + 7 = 91 = 6*14 + 7 = 6*A014106(2) + 7.

a(3) = a(2) + 24*3 + 6 = 91 + 72 + 6 = 169.

a(-4) = 12*4^2 - 18*4 + 7 = 127 = 2*64 - 1 = 2*A085473(3) - 1.

MATHEMATICA

Table[12*n^2 + 18*n + 7, {n, 0, 42}] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)

LinearRecurrence[{3, -3, 1}, {7, 37, 91}, 25] (* G. C. Greubel, Sep 02 2016 *)

PROG

(MAGMA) [ 12*n^2+18*n+7: n in [0..40] ];

(PARI) a(n)=12*n^2+18*n+7 \\ Charles R Greathouse IV, Sep 02 2016

CROSSREFS

Cf. A014106, A153286, A085473.

Sequence in context: A031395 A138906 A107938 * A159491 A106064 A038862

Adjacent sequences:  A154102 A154103 A154104 * A154106 A154107 A154108

KEYWORD

nonn,easy

AUTHOR

Klaus Brockhaus, Jan 04 2009

STATUS

approved

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Last modified September 28 16:19 EDT 2016. Contains 276601 sequences.