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A213630 a(t_1 t_2...t_n) = (t_1 + t_2)*t_1 t_2 + ... + (t_n-1 + t_n)*t_n-1 t_n. 1
1, 4, 9, 16, 25, 36, 49, 64, 81, 10, 22, 36, 52, 70, 90, 112, 136, 162, 190, 40, 63, 88, 115, 144, 175, 208, 243, 280, 319, 90, 124, 160, 198, 238, 280, 324, 370, 418, 468, 160, 205, 252, 301, 352, 405, 460, 517, 576, 637, 250, 306, 364, 424, 486, 550, 616 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Differs from A057147 first at n=100.

a(n)/n = {1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, ...}. - Alexander R. Povolotsky, Jun 19 2012

LINKS

Felipe Bottega Diniz and T. D. Noe, Table of n, a(n) for n = 1..1000 (first 100 terms from Felipe Bottega Diniz)

F. B. Diniz, About a New Family of Sequences, arXiv:1607.06082 [math.GM], 2016.

FORMULA

Let t_1t_2...t_n be a natural number.

a(t_1t_2...t_n) = (t_1 + t_2)*t_1t_2 + ... + (t_n-1 + t_n)*t_n-1t_n, if n even.

If n is odd, t_1 t_2...t_n <- 0t_1t_2...t_n and do a(0t_1 t_2...t_n).

EXAMPLE

a(123456) = (1+2)*12 + (3+4)*34 + (5+6)*56 = 890.

a(890) = (0+8)*08 + (9+0)*90 = 874.

a(15) = (1+5)*15 = 90.

a(7) = (0+7)*07 = 49.

MAPLE

read("transforms"):

A213630 := proc(n)

    local dgs, a, i ;

    if n < 10 then

        n^2;

    else

        dgs := convert(n, base, 10) ;

        a := 0 ;

        for i from 2 to nops(dgs) do

            a := a+(op(i-1, dgs)+op(i, dgs))*digcat2(op(i, dgs), op(i-1, dgs)) ;

        end do:

        a;

    end if;

end proc: # R. J. Mathar, Aug 10 2012

MATHEMATICA

num[n_] := Module[{d = IntegerDigits[n], d2}, If[OddQ[Length[d]], d = Prepend[d, 0]]; d2 = Partition[d, 2]; Sum[(d2[[i, 1]] + d2[[i, 2]])*(10*d2[[i, 1]] + d2[[i, 2]]), {i, Length[d2]}]]; Table[num[n], {n, 100}] (* T. D. Noe, Jun 19 2012 *)

CROSSREFS

Sequence in context: A048385 A230101 A057147 * A061205 A290934 A048387

Adjacent sequences:  A213627 A213628 A213629 * A213631 A213632 A213633

KEYWORD

easy,nonn,base

AUTHOR

Felipe Bottega Diniz, Jun 16 2012

STATUS

approved

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Last modified April 12 00:24 EDT 2021. Contains 342912 sequences. (Running on oeis4.)