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

1,1

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(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

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 k-th triangular number.

Prog

(PARI) Vec(-x*(x-3)^2/((x-1)*(x^2-6*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