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.

9, 57, 337, 1969, 11481, 66921, 390049, 2273377, 13250217, 77227929, 450117361, 2623476241, 15290740089, 89120964297, 519435045697, 3027489309889, 17645500813641, 102845515571961, 599427592618129, 3493720040136817, 20362892648202777, 118683635849079849

Offset: 1

Author

Colin Barker, Sep 24 2015

Keywords

• nonn
• easy

Comments

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

Examples

			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 k-th triangular number.
		

Links

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

Crossrefs

Cf. A000217, A202391, A262489, A262491, A262492.

Programs

PARI

Vec(-x*(x-3)^2/((x-1)*(x^2-6*x+1)) + O(x^30))

Formula

a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>3.

G.f.: -x*(x-3)^2 / ((x-1)*(x^2-6*x+1)).

a(n) = -1+(1-1/sqrt(2))*(3-2*sqrt(2))^n+(1+1/sqrt(2))*(3+2*sqrt(2))^n. - Colin Barker, Mar 05 2016