A369152 Total number of digits in row n of Pascal's triangle.

1, 2, 3, 4, 5, 8, 10, 12, 14, 18, 25, 28, 31, 38, 44, 50, 57, 64, 69, 76, 88, 96, 102, 114, 125, 134, 142, 154, 166, 178, 191, 202, 215, 230, 244, 256, 268, 288, 303, 316, 334, 356, 372, 388, 411, 428, 447, 470, 490, 506, 529, 554, 573, 590, 618, 642, 660, 686

Offset: 0

Author

Bartlomiej Pawlik, Jan 14 2024

Keywords

• nonn
• base

Crossrefs

Cf. A007318, A055642, A003590.

Programs

Maple

a:= n-> length(cat(seq(binomial(n,k), k=0..n))):
seq(a(n), n=0..57);  # Alois P. Heinz, Jan 15 2024

Mathematica

A369152[n_Integer] := Total[IntegerLength[Binomial[n, #]] & /@ Range[0, n]]
First50Terms = Table[A369152[n], {n, 0, 49}]

PARI

a(n) = #concat(vector(n+1, k, Str(binomial(n,k-1)))); \\ Michel Marcus, Jan 18 2024

Python

from math import comb
def A369152(n): return sum(len(str(comb(n,k))) for k in range(n+1)) # Chai Wah Wu, Feb 15 2024

Formula

a(n) = 1 + n + Sum_{k=0..n} floor(log_10(C(n,k))).

a(n) = A055642(A003590(n)). - Michel Marcus, Jan 15 2024