cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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.

Original entry on oeis.org

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
Offset: 1

Views

Author

Colin Barker, Sep 24 2015

Keywords

Comments

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

Examples

			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 k-th triangular number.

Links

Crossrefs

Cf. A000217, A165517, A262490, A262491, A262492.

Programs

  • PARI
    Vec(-x*(x^4-x^3-10*x^2+11*x+7)/((x-1)*(x^4-10*x^2+1)) + O(x^30))

Formula

a(n) = a(n-1)+10*a(n-2)-10*a(n-3)-a(n-4)+a(n-5) for n>5.
G.f.: -x*(x^4-x^3-10*x^2+11*x+7) / ((x-1)*(x^4-10*x^2+1)).

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.

Original entry on oeis.org

9, 57, 337, 1969, 11481, 66921, 390049, 2273377, 13250217, 77227929, 450117361, 2623476241, 15290740089, 89120964297, 519435045697, 3027489309889, 17645500813641, 102845515571961, 599427592618129, 3493720040136817, 20362892648202777, 118683635849079849
Offset: 1

Views

Author

Colin Barker, Sep 24 2015

Keywords

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

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

A262492 The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of thirteen consecutive positive triangular numbers.

Original entry on oeis.org

25, 90, 207, 1117, 2560, 9255, 21202, 114022, 261195, 944020, 2162497, 11629227, 26639430, 96280885, 220553592, 1186067232, 2716960765, 9819706350, 22494303987, 120967228537, 277103358700, 1001513766915, 2294198453182, 12337471243642, 28261825626735
Offset: 1

Views

Author

Colin Barker, Sep 24 2015

Keywords

Comments

For the index of the first of the corresponding thirteen consecutive triangular numbers, see A257293.

Examples

			25 is in the sequence because T(25)+T(26) = 325+351 = 676 = 6+...+120 = T(3)+...+T(15), where T(k) is the k-th triangular number.

Links

Crossrefs

Cf. A000217, A257293, A262489, A262490, A262491.

Programs

  • PARI
    Vec(-x*(12*x^8+13*x^6+65*x^5-1107*x^4+910*x^3+117*x^2+65*x+25)/((x-1)*(x^4-10*x^2-1)*(x^4+10*x^2-1)) + O(x^30))

Formula

G.f.: -x*(12*x^8+13*x^6+65*x^5-1107*x^4+910*x^3+117*x^2+65*x+25) / ((x-1)*(x^4-10*x^2-1)*(x^4+10*x^2-1)).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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