A111707 a(n) = Sum_{k = 1..ceiling(w/2)} d(k) * d(w+1-k), where (d(1), ..., d(w)) is the decimal expansion of n.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8

Offset: 0

Author

Amarnath Murthy, Aug 22 2005

Keywords

• base
• easy
• nonn

Examples

			a(12) = 1*2 = 2, a(12345) = 1*5 + 2*4 + 3*3 = 22.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A085942.

Programs

Mathematica

Array[Sum[#1[[k]]*#1[[#2 + 1 - k]], {k, Ceiling[#2/2]}] & @@ {IntegerDigits[#], IntegerLength[#]} &, 82, 0] (* Michael De Vlieger, May 21 2021 *)

PARI

a(n) = { my (d=digits(n)); sum (k=1, ceil(#d/2), d[k]*d[#d+1-k]) } \\ Rémy Sigrist, May 21 2021

Extensions

More terms from Joshua Zucker, May 08 2006

a(0) = 0 prepended and name clarified by Rémy Sigrist, May 21 2021