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A126335 a(n) = n*(4*n^2+5*n-3)/2. 1
3, 23, 72, 162, 305, 513, 798, 1172, 1647, 2235, 2948, 3798, 4797, 5957, 7290, 8808, 10523, 12447, 14592, 16970, 19593, 22473, 25622, 29052, 32775, 36803, 41148, 45822, 50837, 56205, 61938, 68048, 74547, 81447, 88760, 96498, 104673, 113297 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Inner product of two arithmetic series (A016777, A005408): (1,4,7,...,3n-2)*(3,5,7,...,2n+1) = sum((3i-2)*(2i+1),i=1...n) = 1*3+4*3+7*7+...+(3n-2)*(2n+1) = (1/2)*n*(4*n^2+5*n-3).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(1)=3, a(2)=23, a(3)=72, a(4)=162; for n>4, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4).

G.f.: x*(3 + 11*x - 2*x^2)/(1 - x)^4.

MATHEMATICA

CoefficientList[Series[(3 + 11 x - 2 x^2)/(1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 12 2013 *)

PROG

(PARI) a(n) = n*(4*n^2 + 5*n - 3)/2; \\ Michel Marcus, Oct 11 2013

(MAGMA) [n*(4*n^2+5*n-3)/2: n in [1..40]]; // Vincenzo Librandi, Oct 12 2013

CROSSREFS

Sequence in context: A096207 A163210 A163211 * A256329 A196649 A027701

Adjacent sequences:  A126332 A126333 A126334 * A126336 A126337 A126338

KEYWORD

nonn,easy

AUTHOR

Zak Seidov, Mar 11 2007

STATUS

approved

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Last modified January 17 00:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)