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A215631
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Triangle read by rows: T(n,k) = n^2 + n*k + k^2, 1 <= k <= n.
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11
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3, 7, 12, 13, 19, 27, 21, 28, 37, 48, 31, 39, 49, 61, 75, 43, 52, 63, 76, 91, 108, 57, 67, 79, 93, 109, 127, 147, 73, 84, 97, 112, 129, 148, 169, 192, 91, 103, 117, 133, 151, 171, 193, 217, 243, 111, 124, 139, 156, 175, 196, 219, 244, 271, 300, 133, 147, 163
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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G.f. for triangle: (3-2*x+3*x*y+x^2-11*x^2*y+4*x^3*y+x^3*y^2+x^4*y^2)*x*y/((1-x)^3*(1-x*y)^3). - Robert Israel, May 10 2015
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EXAMPLE
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The triangle begins:
row n T(n,k), 1 <= k <= n
1: 3
2: 7 12
3: 13 19 27
4: 21 28 37 48
5: 31 39 49 61 75
6: 43 52 63 76 91 108
7: 57 67 79 93 109 127 147
8: 73 84 97 112 129 148 169 192
9: 91 103 117 133 151 171 193 217 243
10: 111 124 139 156 175 196 219 244 271 300
11: 133 147 163 181 201 223 247 273 301 331 363
12: 157 172 189 208 229 252 277 304 333 364 397 432
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MAPLE
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seq(seq(i^2+i*j+j^2, j=1..i), i=1..10); # Robert Israel, May 10 2015
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MATHEMATICA
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PROG
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(Haskell)
a215631 n k = a215631_tabl !! (n-1) !! (k-1)
a215631_row n = a215631_tabl !! (n-1)
a215631_tabl = zipWith3 (zipWith3 (\u v w -> u + v + w))
a093995_tabl a075362_tabl a133819_tabl
(PARI) for(n=1, 15, for(k=1, n, print1(n^2+n*k+k^2, ", "))) \\ Derek Orr, May 13 2015
(Magma) [[i^2+i*j+j^2: j in [1..i]]: i in [1..10]]; // Vincenzo Librandi, Jun 07 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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