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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(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

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Last modified September 24 14:33 EDT 2021. Contains 347643 sequences. (Running on oeis4.)