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A003982
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Table read by rows: 1 if x = y, 0 otherwise, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...
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2
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1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Also called the delta function.
(Start) In rectangular format, the infinite identity matrix and the weight array of A003783(n,k)=min{n,k}; in the accumulation chain
... < A003982 < A003783 < A115262 < A185957 <.... See A144112 for definitions of weight array and accumulation array. (End) [From Clark Kimberling, ck6(AT)evansville.edu Feb 7 2011]
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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n-th 1 is followed by 4n-1 0's.
G.f.: 1/(1 - xy). E.g.f.: exp(xy).
Considered as a linear sequence, expansion of q^(-1/2)eta(q^8)^2/eta(q^4) in powers of q. If A(x) is the g.f., then B(x)=(x*A(x^2))^2 satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u, v, w)=u^2*w -v^3 -4*v*w^2. Also, given g.f. A(x), then B(x)=x*A(x^2) satisfies 0=f(B(x), B(x^2), B(x^3), B(x^6)) where f(u1, u2, u3, u6)=u1*u2^2*u6 - u1*u6^3 - u3^3*u2. - Michael Somos Apr 13 2005
a(n)=b(2n+1) where b(n) is multiplicative and b(2^e)=0^e, b(p^e)=(1+(-1)^e)/2 if p>2. - Michael Somos Jun 06 2005
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EXAMPLE
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1; 0,0; 0,1,0; 0,0,0,0; 0,0,1,0,0; ....
Northwest corner when formatted as a rectangular array:
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
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MATHEMATICA
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f[n_, k_]:=0; f[n_, n_]:=1;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 10}]] (* array *)
Table[f[n-k+1, k], {n, 10}, {k, n, 1, -1}]//Flatten (*sequence *)
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PROG
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(PARI) a(n)=issquare(2*n+1) /* Michael Somos Apr 13 2005 */
(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff(eta(x^8+A)^2/eta(x^4+A), n))
(PARI) A(i, j)=i==j
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CROSSREFS
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Characteristic function of A001844. Antidiagonal sums and main diagonal is A000012.
Sequence in context: A014065 A014049 A016371 * A126010 A015857 A016343
Adjacent sequences: A003979 A003980 A003981 * A003983 A003984 A003985
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KEYWORD
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tabl,nonn,nice,easy
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AUTHOR
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Marc LeBrun
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STATUS
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approved
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