

A262490


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


4



9, 57, 337, 1969, 11481, 66921, 390049, 2273377, 13250217, 77227929, 450117361, 2623476241, 15290740089, 89120964297, 519435045697, 3027489309889, 17645500813641, 102845515571961, 599427592618129, 3493720040136817, 20362892648202777, 118683635849079849
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

For the index of the first of the corresponding four consecutive triangular numbers, see A202391.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (7,7,1).


FORMULA

a(n) = 7*a(n1)7*a(n2)+a(n3) for n>3.
G.f.: x*(x3)^2 / ((x1)*(x^26*x+1)).
a(n) = 1+(11/sqrt(2))*(32*sqrt(2))^n+(1+1/sqrt(2))*(3+2*sqrt(2))^n.  Colin Barker, Mar 05 2016


EXAMPLE

9 is in the sequence because T(9)+T(10) = 45+55 = 100 = 15+21+28+36 = T(5)+T(6)+T(7)+T(8), where T(k) is the kth triangular number.


PROG

(PARI) Vec(x*(x3)^2/((x1)*(x^26*x+1)) + O(x^30))


CROSSREFS

Cf. A000217, A202391, A262489, A262491, A262492.
Sequence in context: A026896 A080961 A163919 * A180028 A155605 A199485
Adjacent sequences: A262487 A262488 A262489 * A262491 A262492 A262493


KEYWORD

nonn,easy


AUTHOR

Colin Barker, Sep 24 2015


STATUS

approved



