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 A173920 Triangle read by rows: T(n,k) = convolution of n with k in binary representation, 0<=k<=n. 7
 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 0, 1, 1, 2, 1, 2, 2, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 0, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 3, 1, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS T(n,k) = SUM(bn(i)*bk(L-i-1): 0<=i0; T(n,2) = A079944(n-2) for n>1; T(n,3) = A079882(n-2) for n>2; T(n,4) = A173922(n-4) for n>3; T(n,8) = A173923(n-8) for n>7; T(n,n) = A159780(n). LINKS R. Zumkeller, Rows 0 to 320 of the triangle, flattened FORMULA T(n,k) = c(A030101(n),k,0) with c(x,y,z) = if y=0 then z else c([x/2],[y/2],z+(x mod 2)*(y mod 2)). EXAMPLE T(13,10) = T('1101','1010') = 1*0 + 1*1 + 0*0 + 1*1 = 2; T(13,11) = T('1101','1011') = 1*1 + 1*1 + 0*0 + 1*1 = 3; T(13,12) = T('1101','1100') = 1*0 + 1*0 + 0*1 + 1*1 = 1; T(13,13) = T('1101','1101') = 1*1 + 1*0 + 0*1 + 1*1 = 2. Triangle begins:   0;   0, 1;   0, 1, 0;   0, 1, 1, 2;   0, 1, 0, 1, 0;   0, 1, 0, 1, 1, 2;   ... MATHEMATICA T[n_, k_] := Module[{bn, bk, lg},      bn = IntegerDigits[n, 2];      bk = IntegerDigits[k, 2];      lg = Max[Length[bn], Length[bk]];      ListConvolve[PadLeft[bn, lg], PadLeft[bk, lg]]][[1]]; Table[T[n, k], {n, 0, 13}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 19 2021 *) CROSSREFS Sequence in context: A112378 A324832 A035203 * A230001 A070100 A070095 Adjacent sequences:  A173917 A173918 A173919 * A173921 A173922 A173923 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Mar 04 2010 STATUS approved

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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)