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Search: id:A157014
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| A157014 |
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The general form of the recurrences are the a(j) , b(j) and n(j) solutions of the 2 equations problem : A*n(j)+1 = a(j)*a(j) ; (A+1)*n(j)+1 = b(j)*b(j) ; with A, n(j), a(j), b(j) positive integer elements. The example above is the a(j) recurrence for A=5. |
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11
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OFFSET
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1,2
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COMMENT
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For some other values of A the a(j),b(j) and n(j) sequences are already known
A a-sequence b-sequence n-sequence
1 A001653 A002315 A078522
2 A072256 A054320 A045502
3 A001570 A028230 A059989
4 A007805 A049629 -
5 - A133283 -
6 A153111 - -
7 - - -
8 A077420 A046176 -
9 A097315 A097314 -
For all higher values of A, no sequences could be found in your list.
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FORMULA
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the a(j) recurrence is a(1)=1 ; a(2)=4*A+1 ; a(t+2)=(4*A+2)*a(t+1)-a(t) ; resulting in a(j) terms 1, 4*A+1, 16*A*A+12*A+1, 64*A*A*A+80*A*A+24*A+1 the b(j) recurrence is b(1)=1 ; b(2)=4*A+3; b(t+2)=(4*A+2)*b(t+1)-b(t); resulting in b(j) terms 1, 4*A+3, 16*A*A+20*A+5, 64A*A*A+112*A*A+56*A+7 the n(j) recurrence is n(1)=0 ; n(2)=16*A+8 ; n(3)=(16*A*A+16*A+3)*n(2) ; n(t+3)=(16*A*A+16*A+3)*(n(t+2)-n(t+1)) + n(t) ; resulting in n(j) terms 0, 16*A+8, 128*A*A*A+384*A*A+176*A+24, 4096*A*A*A*A*A+10240*A*A*A*A+9472*A*A*A+3968*A*A+736*A*A+48
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CROSSREFS
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Sequence in context: A167255 A009965 A041842 this_sequence A076552 A126996 A158603
Adjacent sequences: A157011 A157012 A157013 this_sequence A157015 A157016 A157017
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KEYWORD
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nonn
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AUTHOR
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Paul Weisenhorn (paulweisenhorn(AT)online.de), Feb 21 2009
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