OFFSET
1,2
LINKS
T. D. Noe, Table of n, a(n) for n=1..1023
FORMULA
G.f.: 1/(1-x) * Sum_{k>=0} (k+1)^2*x^2^k/(1+x^2^k). - Ralf Stephan, Jun 23 2003
EXAMPLE
To get a(5), we write 10 = 2 + 8 = 2^1 + 2^3 so a(5) = 1^2 + 3^2 = 10.
MAPLE
a:= n-> (l-> add(l[i]*i^2, i=1..nops(l)))(convert(n, base, 2)):
seq(a(n), n=1..80); # Alois P. Heinz, Nov 20 2019
MATHEMATICA
a[n_] := Total[Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]]^2]; Table[a[n], {n, 1, 70}] (* Jean-François Alcover Mar 21 2011 *)
PROG
(C)
#include <stdio.h>
#include <stdlib.h>
#define USAGE "Usage: 'A008935 num'\n where num is the index of the desired ending value in the sequence.\n"
#define MAX 1023
#define SHIFT_MAX 9
int main(int argc, char *argv[]) { unsigned short mask, i, j, end; unsigned long sum; if (argc < 2) { fprintf(stderr, USAGE); return EXIT_FAILURE; } end = atoi(argv[1]); end = (end >= MAX) ? MAX : end;
fprintf(stdout, "Values: "); for (i = 1; i <= end; i++) { sum = 0; mask = 1; for (j = 0; j < SHIFT_MAX; j++, mask *= 2) if (i & mask) sum += (j+1) * (j+1); fprintf(stdout, "%ld", sum); if (i < end) fprintf(stdout, ", "); } fprintf(stdout, "\n"); return EXIT_SUCCESS; }
(Haskell)
a008935 = f 1 where
f k x | x == 0 = 0
| r == 0 = f (k+1) x'
| otherwise = k^2 + f (k+1) x' where (x', r) = divMod x 2
-- Reinhard Zumkeller, Jul 05 2011
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
Corrected and extended by Larry Reeves (larryr(AT)acm.org), Mar 22 2000
STATUS
approved