login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A191347 Array read by antidiagonals: ((floor(sqrt(n)) + sqrt(n))^k + (floor(sqrt(n)) - sqrt(n))^k)/2 for columns k >= 0 and rows n >= 0. 3
1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 4, 3, 1, 1, 0, 8, 7, 4, 2, 1, 0, 16, 17, 10, 8, 2, 1, 0, 32, 41, 28, 32, 9, 2, 1, 0, 64, 99, 76, 128, 38, 10, 2, 1, 0, 128, 239, 208, 512, 161, 44, 11, 2, 1, 0, 256, 577, 568, 2048, 682, 196, 50, 12, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Table of n, a(n) for n=0..65.

FORMULA

For each row n>=0 let T(n,0)=1 and T(n,1)=floor(sqrt(n)), then for each column k>=2: T(n,k)=T(n,k-2)*(n-T(n,1)^2) + T(n,k-1)*T(n,1)*2. - Charles L. Hohn, Aug 22 2019

T(n, k) = Sum_(i=0, floor((k+1)/2), binomial(k, 2*i)*floor(sqrtint(n))^(k-2*i)*n^i)) for n > 0, with T(0, 0) = 1 and T(0, k) = 0 for k > 0. - Michel Marcus, Aug 23 2019

EXAMPLE

1, 0,  0,   0,    0,    0,     0,      0,       0,        0,        0, ...

1, 1,  2,   4,    8,   16,    32,     64,     128,      256,      512, ...

1, 1,  3,   7,   17,   41,    99,    239,     577,     1393,     3363, ...

1, 1,  4,  10,   28,   76,   208,    568,    1552,     4240,    11584, ...

1, 2,  8,  32,  128,  512,  2048,   8192,   32768,   131072,   524288, ...

1, 2,  9,  38,  161,  682,  2889,  12238,   51841,   219602,   930249, ...

1, 2, 10,  44,  196,  872,  3880,  17264,   76816,   341792,  1520800, ...

1, 2, 11,  50,  233, 1082,  5027,  23354,  108497,   504050,  2341691, ...

1, 2, 12,  56,  272, 1312,  6336,  30592,  147712,   713216,  3443712, ...

1, 3, 18, 108,  648, 3888, 23328, 139968,  839808,  5038848, 30233088, ...

1, 3, 19, 117,  721, 4443, 27379, 168717, 1039681,  6406803, 39480499, ...

1, 3, 20, 126,  796, 5028, 31760, 200616, 1267216,  8004528, 50561600, ...

1, 3, 21, 135,  873, 5643, 36477, 235791, 1524177,  9852435, 63687141, ...

1, 3, 22, 144,  952, 6288, 41536, 274368, 1812352, 11971584, 79078912, ...

1, 3, 23, 153, 1033, 6963, 46943, 316473, 2133553, 14383683, 96969863, ...

...

PROG

(PARI) T(n, k) = if (n==0, k==0, my(x=sqrtint(n)); sum(i=0, (k+1)\2, binomial(k, 2*i)*x^(k-2*i)*n^i));

matrix(9, 9, n, k, T(n-1, k-1)) \\ Michel Marcus, Aug 22 2019

(PARI) T(n, k) = if (k==0, 1, if (k==1, sqrtint(n), T(n, k-2)*(n-T(n, 1)^2) + T(n, k-1)*T(n, 1)*2));

matrix(9, 9, n, k, T(n-1, k-1)) \\ Charles L. Hohn, Aug 22 2019

CROSSREFS

Row 1 is A000007, row 2 is A011782, row 3 is A001333, row 4 is A026150, row 5 is A081294, row 6 is A001077, row 7 is A084059, row 8 is A108851, row 9 is A084128, row 10 is A081341, row 11 is A005667, row 13 is A141041.

Row 3*2 is A002203, row 4*2 is A080040, row 5*2 is A155543, row 6*2 is A014448, row 8*2 is A080042, row 9*2 is A170931, row 11*2 is A085447.

Cf. A191348 which uses ceiling() in place of floor().

Sequence in context: A318686 A214546 A255704 * A106234 A238125 A062507

Adjacent sequences:  A191344 A191345 A191346 * A191348 A191349 A191350

KEYWORD

nonn,tabl

AUTHOR

Charles L. Hohn, May 31 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)