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A180223 a(n) = (11*n^2 - 7*n)/2. 9
0, 2, 15, 39, 74, 120, 177, 245, 324, 414, 515, 627, 750, 884, 1029, 1185, 1352, 1530, 1719, 1919, 2130, 2352, 2585, 2829, 3084, 3350, 3627, 3915, 4214, 4524, 4845, 5177, 5520, 5874, 6239, 6615, 7002, 7400, 7809, 8229, 8660 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This sequence is related to A050441 by n*a(n)-sum(a(i), i=0..n-1) = 2*A050441(n). - Bruno Berselli, Aug 19 2010

Sum of n-th heptagonal number (A000566) and n-th octagonal number (A000567). - Bruno Berselli, Jun 11 2013

Create a triangle with T(r,1) = r^2 and T(r,c) = r^2 + r*c + c^2. The difference of the sum of the terms in row n and those in row n-1 is a(n). - J. M. Bergot, Jun 17 2013

LINKS

B. Berselli, Table of n, a(n) for n = 0..10000.

B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).

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

FORMULA

G.f.: x*(2+9*x)/(1-x)^3. - Bruno Berselli, Aug 19 2010 - corrected in Apr 18 2011

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) with n>2. - Bruno Berselli, Aug 19 2010

a(n) = n + A226492(n). - Bruno Berselli, Jun 11 2013

E.g.f.: (1/2)*x*(11*x + 4) * exp(x). - G. C. Greubel, Aug 24 2015

MAPLE

A180223:=n->(11*n^2 - 7*n)/2; seq(A180223(n), n=0..30); # Wesley Ivan Hurt, Feb 25 2014

MATHEMATICA

Table[(11*n^2 - 7*n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Feb 25 2014 *)

PROG

(PARI) a(n)=1/2*(11*n^2 - 7*n);

(MAGMA) [(11*n^2 - 7*n)/2: n in [0..30]]; // Vincenzo Librandi, Apr 18 2011

CROSSREFS

Cf. A050441, A000566, A000567, A226492.

Cf. numbers of the form n*(n*k-k+4))/2 listed in A226488 (this sequence is the case k=11). - Bruno Berselli, Jun 10 2013

Sequence in context: A007217 A295367 A214541 * A070009 A070170 A033568

Adjacent sequences:  A180220 A180221 A180222 * A180224 A180225 A180226

KEYWORD

nonn,easy

AUTHOR

Graziano Aglietti (mg5055(AT)mclink.it), Aug 16 2010

STATUS

approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)