A267238 Sum of the triangular numbers whose indices are the digits of n.

1, 3, 6, 10, 15, 21, 28, 36, 45, 1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 3, 4, 6, 9, 13, 18, 24, 31, 39, 48, 6, 7, 9, 12, 16, 21, 27, 34, 42, 51, 10, 11, 13, 16, 20, 25, 31, 38, 46, 55, 15, 16, 18, 21, 25, 30, 36, 43, 51, 60, 21, 22, 24, 27, 31, 36, 42, 49, 57, 66, 28, 29, 31, 34, 38, 43, 49, 56, 64, 73, 36, 37, 39, 42, 46, 51, 57, 64, 72, 81

Offset

1,2

Links

Table of n, a(n) for n=1..89.

Formula

From Robert Israel, Jan 21 2016: (Start)

G.f.: A(x) = Sum_{j >= 0} (1-x^(10^j))/((1-x)*(1-x^(10^(j+1)))) * Sum_{d=1..9} d*(d+1)/2 * x^(d*10^j)

satisfies A(x) = (1-x^10)*A(x^10)/(1-x) + (1+3*x^2+6*x^3+10*x^4+15*x^5+21*x^6+28*x^7+36*x^8+45*x^9)/(1-x^10).

a(10*m + j) = a(m) + j*(j+1)/2 for 0 <= j <= 9. (End)

Example

a(12) = 1*2/2 + 2*3/2 = 4.

Maple

seq(add(d*(d+1)/2, d = convert(n, base, 10)), n=1..1000); # Robert Israel, Jan 21 2016

Mathematica

f[n_]:=Total[IntegerDigits[n]*(IntegerDigits[n]+1)/2]; f/@Range@100

Prog

(PARI) a(n) = {my(d = digits(n)); sum(k=1, #d, d[k]*(d[k]+1)/2); } \\ Michel Marcus, Jan 12 2016

Crossrefs

Cf. A000217, A266998, A266999.

Sequence in context: A033441 A338334 A107082 * A256379 A187845 A130488

Adjacent sequences: A267235 A267236 A267237 * A267239 A267240 A267241

Keyword

base,easy,nonn

Author

Ivan N. Ianakiev, Jan 12 2016

Status

approved