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A214659 a(n) = n*(7*n^2 - 3*n - 1)/3. 3
0, 1, 14, 53, 132, 265, 466, 749, 1128, 1617, 2230, 2981, 3884, 4953, 6202, 7645, 9296, 11169, 13278, 15637, 18260, 21161, 24354, 27853, 31672, 35825, 40326, 45189, 50428, 56057, 62090, 68541, 75424, 82753, 90542, 98805, 107556, 116809, 126578, 136877 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = sum of n-th row of triangle A214604 for n > 0.

a(n) = A051673(n) + A002378(n).

a(n) = the sum of the n X n matrices of A204008. For example, for n = 3, the sum of the 9 elements of the 3 X 3 submatrix of A204008 is 1 + 4 + 7 + 4 + 5 + 8 + 7 + 8 + 9 = 53. - J. M. Bergot, Jul 15 2013

LINKS

Table of n, a(n) for n=0..39.

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

FORMULA

From Wesley Ivan Hurt, Apr 11 2015: (Start)

a(n) = (7*n^3-3*n^2-n)/3.

G.f.: x*(1+10*x+3*x^2)/(x-1)^4.

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). (End)

MAPLE

A214659:=n->(7*n^3-3*n^2-n)/3: seq(A214659(n), n=0..50); # Wesley Ivan Hurt, Apr 11 2015

MATHEMATICA

Table[(7 n^3 - 3 n^2 - n)/3, {n, 0, 50}] (* Wesley Ivan Hurt, Apr 11 2015 *)

PROG

(Haskell)

a214659 n = ((7 * n - 3) * n - 1) * n `div` 3

(MAGMA) [(7*n^3-3*n^2-n)/3 : n in [0..50]]; // Wesley Ivan Hurt, Apr 11 2015

CROSSREFS

Cf. A002378, A051673, A204008, A214604, A214675.

Sequence in context: A332594 A338165 A217077 * A241354 A240811 A118856

Adjacent sequences:  A214656 A214657 A214658 * A214660 A214661 A214662

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Jul 25 2012

STATUS

approved

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Last modified June 15 12:29 EDT 2021. Contains 345048 sequences. (Running on oeis4.)