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A081268 Diagonal of triangular spiral in A051682. 4
1, 12, 32, 61, 99, 146, 202, 267, 341, 424, 516, 617, 727, 846, 974, 1111, 1257, 1412, 1576, 1749, 1931, 2122, 2322, 2531, 2749, 2976, 3212, 3457, 3711, 3974, 4246, 4527, 4817, 5116, 5424, 5741, 6067, 6402, 6746, 7099, 7461, 7832, 8212, 8601, 8999, 9406 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..45.

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

FORMULA

a(n) = C(n, 0) + 11C(n, 1) + 9C(n, 2); binomial transform of (1, 11, 9, 0, 0, 0, ...).

a(n) = (9n^2 + 13n+2)/2.

G.f.: (1 + 9x - x^2)/(1-x)^3.

a(n) = 9*n + a(n-1) + 2 (with a(0)=1). - Vincenzo Librandi, Aug 08 2010

EXAMPLE

a(1) = 9*1 +  1 + 2 = 12;

a(2) = 9*2 + 12 + 2 = 32;

a(3) = 9*3 + 32 + 2 = 61.

PROG

(PARI) a(n)=(9*n^2+13*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A081267.

Sequence in context: A166959 A134582 A177721 * A188183 A183682 A243027

Adjacent sequences:  A081265 A081266 A081267 * A081269 A081270 A081271

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 15 2003

STATUS

approved

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Last modified November 20 02:57 EST 2018. Contains 317371 sequences. (Running on oeis4.)