

A262489


The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of three consecutive positive triangular numbers.


4



7, 18, 78, 187, 781, 1860, 7740, 18421, 76627, 182358, 758538, 1805167, 7508761, 17869320, 74329080, 176888041, 735782047, 1751011098, 7283491398, 17333222947, 72099131941, 171581218380, 713707828020, 1698478960861, 7064979148267, 16813208390238
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OFFSET

1,1


COMMENTS

For the index of the first of the corresponding three consecutive triangular numbers, see A165517.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,10,10,1,1).


FORMULA

a(n) = a(n1)+10*a(n2)10*a(n3)a(n4)+a(n5) for n>5.
G.f.: x*(x^4x^310*x^2+11*x+7) / ((x1)*(x^410*x^2+1)).


EXAMPLE

7 is in the sequence because T(7)+T(8) = 28+36 = 64 = 15+21+28 = T(5)+T(6)+T(7), where T(k) is the kth triangular number.


PROG

(PARI) Vec(x*(x^4x^310*x^2+11*x+7)/((x1)*(x^410*x^2+1)) + O(x^30))


CROSSREFS

Cf. A000217, A165517, A262490, A262491, A262492.
Sequence in context: A304142 A019534 A024830 * A030982 A203381 A207158
Adjacent sequences: A262486 A262487 A262488 * A262490 A262491 A262492


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Sep 24 2015


STATUS

approved



