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A127736 a(n) = n*(n^2+2*n-1)/2. 7
1, 7, 21, 46, 85, 141, 217, 316, 441, 595, 781, 1002, 1261, 1561, 1905, 2296, 2737, 3231, 3781, 4390, 5061, 5797, 6601, 7476, 8425, 9451, 10557, 11746, 13021, 14385, 15841, 17392, 19041, 20791, 22645, 24606, 26677, 28861, 31161, 33580, 36121, 38787, 41581 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums of A127735.

Row sums of A162610. - Reinhard Zumkeller, Jan 19 2013

For n  > 0, a(n) is the number of compositions of n+10 into n parts avoiding parts 2 and 3. - Milan Janjic, Jan 07 2016

LINKS

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

Index to sequences related to polygonal numbers

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

FORMULA

Row sums of triangle A134390. Also, binomial transform of [1, 6, 8, 3, 0, 0, 0,...). - Gary W. Adamson, Oct 23 2007

a(n) = (n+1)*A000217(n)-n = A006002(n)-n. - R. J. Mathar, Jul 21 2009

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: -x*(x^2-3*x-1) / (x-1)^4. - Colin Barker, Mar 12 2014

a(n) = A057145(n+5,n). - R. J. Mathar, Jul 28 2016

MAPLE

A127736:=n->n*(n^2+2*n-1)/2; seq(A127736(n), n=1..40); # Wesley Ivan Hurt, Mar 14 2014

MATHEMATICA

Table[n*(n^2 + 2*n - 1)/2, {n, 60}] (* Vladimir Joseph Stephan Orlovsky, Jun 24 2011 *)

CoefficientList[Series[-(x^2 - 3 x - 1)/(x - 1)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 14 2014 *)

LinearRecurrence[{4, -6, 4, -1}, {1, 7, 21, 46}, 60] (* Harvey P. Dale, Apr 22 2014 *)

PROG

(PARI) Vec(-x*(x^2-3*x-1)/(x-1)^4 + O(x^100)) \\ Colin Barker, Mar 12 2014

(PARI) a(n) = n*(n^2+2*n-1)/2; \\ Altug Alkan, Jan 07 2016

CROSSREFS

Cf. A002260, A127701, A127735, A134390.

Sequence in context: A299254 A146411 A287431 * A212677 A146802 A147054

Adjacent sequences:  A127733 A127734 A127735 * A127737 A127738 A127739

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jan 26 2007

EXTENSIONS

More terms and new name from R. J. Mathar, Jul 21 2009

STATUS

approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)