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A059924
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Write the numbers from 1 to n^2 in a spiraling square; a(n) is the total of the sums of the two diagonals.
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1
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0, 2, 10, 34, 80, 158, 274, 438, 656, 938, 1290, 1722, 2240, 2854, 3570, 4398, 5344, 6418, 7626, 8978, 10480, 12142, 13970, 15974, 18160, 20538, 23114, 25898, 28896, 32118, 35570, 39262, 43200, 47394, 51850, 56578, 61584, 66878, 72466, 78358
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| If n is odd, n^2 is counted twice.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,1000
Index to sequences with linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).
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FORMULA
| a(n) = 3a(n-1)-2a(n-2)-2a(n-3)+3a(n-4)-a(n-5), a(0) = 0, a(1) = 2, a(2) = 10, a(3) = 34, a(4) = 80.
a(n) = (16*n^3 -6*n^2 +8*n +3 -3*(-1)^n)/12. - Frank Ellermann, Mar 16 2002
O.g.f.: (2*x+4*x^2+8*x^3+2*x^4)/(1-3*x+2*x^2+2*x^3-3*x^4+x^5)=(2*x+4*x^2+8*x^3+2*x^4)/((1-x)^4*(1+x)). [From Eric Werley (erw309(AT)lehigh.edu), Jun 30 2011]
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EXAMPLE
| Write the numbers from 1 to 16 like this:
.1 .2 .3 4
12 13 14 5
11 16 15 6
10 .9 .8 7
- the two diagonals add to 36 and 44, so a(4) = 36 + 44 = 80.
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PROG
| (PARI) { for (n=0, 1000, write("b059924.txt", n, " ", floor((16*n^3 - 6*n^2 + 8*n + 3 - 3*(-1^n))/12)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 30 2009]
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CROSSREFS
| Sequence in context: A036369 A043004 A108100 * A022498 A036799 A190161
Adjacent sequences: A059921 A059922 A059923 * A059925 A059926 A059927
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Fabian Rothelius (fabian.rothelius(AT)telia.com), Feb 10 2001
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EXTENSIONS
| Corrected and extended by Eric Werley (erw309(AT)lehigh.edu), Jun 30 2011
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