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A077260
Triangular numbers that are 1/5 of a triangular number.
12
0, 3, 21, 990, 6786, 318801, 2185095, 102652956, 703593828, 33053933055, 226555027545, 10643263790778, 72950015275686, 3427097886697485, 23489678363743371, 1103514876252799416, 7563603483110089800, 355328363055514714491, 2435456831883085172253, 114414629388999485266710
OFFSET
0,2
FORMULA
a(n) = A077261(n)/5.
a(n) = b(n)*(b(n)+1)/2 where b(n) = A077259(n).
a(n) = (A000045(A007310(n+1))^2-1)/8. - Vladeta Jovovic, Nov 02 2002. - Definition corrected by R. J. Mathar, Sep 16 2009
G.f.: (-3*x*(x^2+6*x+1))/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
a(n) = 322*a(n-2) - a(n-4) + 24. - Vladimir Pletser, Mar 23 2020
E.g.f.: (-6*cosh(x) - (-3 + sqrt(5))*cosh((9 - 4*sqrt(5))*x) + (3 + sqrt(5))*cosh((9 + 4*sqrt(5))*x) - 6*sinh(x) + (7 - 3*sqrt(5))*sinh((9 - 4*sqrt(5))*x) + (7 + 3*sqrt(5))*sinh((9 + 4*sqrt(5))*x))/80. - Stefano Spezia, Aug 15 2024
EXAMPLE
Since b(3)=44 -> a(3)=44*45/2=990.
MATHEMATICA
CoefficientList[Series[(-3 x (x^2 + 6 x + 1))/((x - 1) (x^2 - 18 x + 1)*(x^2 + 18 x + 1)), {x, 0, 18}], x] (* Michael De Vlieger, Apr 21 2021 *)
LinearRecurrence[{1, 322, -322, -1, 1}, {0, 3, 21, 990, 6786}, 20] (* Harvey P. Dale, Dec 12 2023 *)
PROG
(PARI) concat(0, Vec(-3*x*(x^2+6*x+1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))) \\ Colin Barker, May 15 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Bruce Corrigan (scentman(AT)myfamily.com), Nov 01 2002
STATUS
approved