A280113 Triangular numbers (A000217) that are also centered 10-gonal numbers (A062786).

1, 1711, 2467531, 3558178261, 5130890585101, 7398740665537651, 10668978908814707911, 15384660187770143270281, 22184669321785637781037561, 31990277777354701910112892951, 46129958370276158368745010598051, 66519367979660443013028395169496861

Offset: 1

Author

Colin Barker, Dec 26 2016

Keywords

• nonn
• easy

Examples

			1711 is in the sequence because the 58th triangular number is 1711, which is also the 19th centered 10-gonal number.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..300
• Index entries for linear recurrences with constant coefficients, signature (1443,-1443,1).

Crossrefs

Cf. A000217, A062786, A280111, A280112.

Programs

Mathematica

RecurrenceTable[{a[n] == 1443 a[n - 1] - 1443 a[n - 2] + a[n - 3], a[1] == 1, a[2] == 1711, a[3] == 2467531}, a, {n, 12}] (* or *)
Rest@ CoefficientList[Series[x (1 + 268 x + x^2)/((1 - x) (1 - 1442 x + x^2)), {x, 0, 12}], x] (* Michael De Vlieger, Dec 26 2016 *)
LinearRecurrence[{1443,-1443,1},{1,1711,2467531},20] (* Harvey P. Dale, Dec 29 2017 *)

PARI

Vec(x*(1 + 268*x + x^2) / ((1 - x)*(1 - 1442*x + x^2)) + O(x^15))

Formula

a(n) = 1443*a(n-1) - 1443*a(n-2) + a(n-3) for n>3.

G.f.: x*(1 + 268*x + x^2) / ((1 - x)*(1 - 1442*x + x^2)).