A222314 Number of characters when n-th row of Pascal's triangle is written in base 10 (including the n spaces).

1, 3, 5, 7, 9, 13, 16, 19, 22, 27, 35, 39, 43, 51, 58, 65, 73, 81, 87, 95, 108, 117, 124, 137, 149, 159, 168, 181, 194, 207, 221, 233, 247, 263, 278, 291, 304, 325, 341, 355, 374, 397, 414, 431, 455, 473, 493, 517, 538, 555, 579, 605, 625, 643, 672, 697, 716, 743, 769, 795, 820, 847, 870, 899, 929, 957, 981, 1011, 1046, 1077, 1107, 1139, 1173

Offset

0,2

Comments

Inspired by Fig. 1 of Cobeli and Zaharescu.

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..2000

C. Cobeli and A. Zaharescu, Promenade around Pascal Triangle-Number Motives, Bull. Math. Soc. Sci. Math. Roumanie, Tome 56(104) No. 1, 2013, 73-98.

N. J. A. Sloane, Triangle showing silhouette of first 30 rows of Pascal's triangle (after Cobeli and Zaharescu)

Formula

Stirling's formula shows that a(n) ~ n^2/(2 log 10) = 0.217... n^2.

Example

"1 6 15 20 15 6 1" contains 16 characters, so a(6) = 16.

Maple

lis:=[];
M:=100;
f1:=n->[seq(binomial(n, k), k=0..n)];
for n from 0 to M do
t1:=f1(n);
t2:=convert(t1, string);
t3:=length(t2)-2-n;
lis:=[op(lis), t3];
od:
[seq(lis[i], i=1..M)];

Prog

(PARI) a(n) = n + sum(k=0, n, #digits(binomial(n, k))); \\ Michel Marcus, Aug 29 2015

Crossrefs

Cf. A007318.

Sequence in context: A243910 A211136 A178653 * A228232 A182058 A200975

Adjacent sequences: A222311 A222312 A222313 * A222315 A222316 A222317

Keyword

nonn,base

Author

N. J. A. Sloane, Feb 16 2013

Status

approved