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A042948
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Congruent to 0 or 1 mod 4.
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35
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0, 1, 4, 5, 8, 9, 12, 13, 16, 17, 20, 21, 24, 25, 28, 29, 32, 33, 36, 37, 40, 41, 44, 45, 48, 49, 52, 53, 56, 57, 60, 61, 64, 65, 68, 69, 72, 73, 76, 77, 80, 81, 84, 85, 88, 89, 92, 93, 96, 97, 100, 101, 104, 105, 108
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Maximum number of squares attacked by a bishop on an n X n chessboard - Stewart Gordon (smjg(AT)iname.com), Mar 23 2001
Also number of squares attacked by a bishop on a toroidal chessboard. - Diego Torres (torresvillarroel(AT)hotmail.com), May 30 2001
Numbers n such that {1,2,3,...,n-1,n} is a perfect Skolem set. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 24 2006
The number of terms which lie on the principal diagonals of an n X n square spiral. - William A. Tedeschi (fynmun(AT)hotmail.com), Mar 02 2008
Possible nonnegative discriminants of quadratic equation a*x^2+b*x+c or discrminants of binary quadratic forms a*x^2+b*x*y+c^y^2. - Artur Jasinski (grafix(AT)csl.pl), Apr 28 2008
A133872(a(n)) = 1; complement of A042964. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 03 2008]
Partial sums of a(n) in A035608(n). A035608(n) = Expansion of x(1+3x)/((1+x)(1-x)^3). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Dec 18 2009]
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REFERENCES
| T. Skolem, On certain distributions of integers in pairs with given differences, Math. Scand., 1957, vol. 5, 57-68.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,1,-1).
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FORMULA
| G.f.: x*(1+3*x)/((1+x)*(1-x)^2). a(n)=a(n-1)+2+(-1)^n - Michael Somos, Jan 12 2000.
a(n)=-1/2+1/2*(-1)^n+2*n, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Oct 03 2008]
A042948 a(n)=4*n-a(n-1)-3 (with a(0)=0) [From Vincenzo Librandi, Nov 17 2010]
a(n)=Sum_k>=0 {A030308(n,k)*A151821(k+1)}. - From DELEHAM Philippe, Oct 17 2011.
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MAPLE
| a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+4 od: seq(a[n], n=0..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
seq(add(irem(3^k, 4), k=4..n), n=3..57); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 20 2008
a:=n->add(2+(-1)^j, j=1..n):seq(a(n), n=0..52); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 13 2008]
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MATHEMATICA
| bb = {}; Do[Do[Do[d = b^2 - 4 a c; If[d < 0, [null], AppendTo[bb, d]], {a, 0, 50}], {b, 0, 50}], {c, 0, 50}]; Union[bb] - Artur Jasinski (grafix(AT)csl.pl), Apr 28 2008
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PROG
| (PARI) a(n)=2*n-n%2
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CROSSREFS
| A042948(n) = A042963(n)-1.
Sequence in context: A042956 A128217 A190671 * A126001 A188085 A206554
Adjacent sequences: A042945 A042946 A042947 * A042949 A042950 A042951
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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