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 A236770 a(n) = n*(n + 1)*(3*n^2 + 3*n - 2)/8. 11
 0, 1, 12, 51, 145, 330, 651, 1162, 1926, 3015, 4510, 6501, 9087, 12376, 16485, 21540, 27676, 35037, 43776, 54055, 66045, 79926, 95887, 114126, 134850, 158275, 184626, 214137, 247051, 283620, 324105, 368776, 417912, 471801, 530740, 595035, 665001, 740962 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS After 0, first trisection of A011779 and right border of A177708. LINKS Bruno Berselli, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: x*(1 + 7*x + x^2)/(1 - x)^5. a(n) = a(-n-1) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). a(n) = A000326(A000217(n)). a(n) = A000217(n) + 9*A000332(n+2). Sum_{n>=1} 1/a(n) = 2 + 4*sqrt(3/11)*Pi*tan(sqrt(11/3)*Pi/2) = 1.11700627139319... . - Vaclav Kotesovec, Apr 27 2016 MATHEMATICA Table[n (n + 1) (3 n^2 + 3 n - 2)/8, {n, 0, 40}] LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 12, 51, 145}, 40] (* Harvey P. Dale, Aug 22 2016 *) PROG (PARI) for(n=0, 40, print1(n*(n+1)*(3*n^2+3*n-2)/8", ")); (MAGMA) [n*(n+1)*(3*n^2+3*n-2)/8: n in [0..40]]; CROSSREFS Partial sums of A004188. Cf. A000217, A000332, A011779, A177708. Cf. similar sequences on the polygonal numbers: A002817(n) = A000217(A000217(n)); A000537(n) = A000290(A000217(n)); A037270(n) = A000217(A000290(n)); A062392(n) = A000384(A000217(n)). Cf. sequences of the form A000217(m)+k*A000332(m+2): A062392 (k=12); A264854 (k=11); A264853 (k=10); this sequence (k=9); A006324 (k=8); A006323 (k=7); A000537 (k=6); A006322 (k=5); A006325 (k=4), A002817 (k=3), A006007 (k=2), A006522 (k=1). Cf. A232713, A260810. Sequence in context: A268351 A166776 A200887 * A115680 A231298 A231359 Adjacent sequences:  A236767 A236768 A236769 * A236771 A236772 A236773 KEYWORD nonn,easy AUTHOR Bruno Berselli, Jan 31 2014 STATUS approved

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Last modified October 15 12:31 EDT 2019. Contains 328026 sequences. (Running on oeis4.)